For the function $f(x)=3 x + 2 \sin(x)$, find all intervals where the function is increasing.
$f$ is increasing on
(Give your answer as an interval or a list of intervals, e.g., (-infinity,8] or (1,5),(7,10) . Enter none if there are no such intervals.)

Similarly, find all intervals where the function is decreasing:
$f$ is decreasing on
(Give your answer as an interval or a list of intervals, e.g., (-infinity,8] or (1,5),(7,10) . Enter none if there are no such intervals.)

Finally, find all critical points in the graph of $f(x)$ (enter $x$ values as a comma-separated list, or none if there are no critical points):